anonymous
  • anonymous
What mathematical induction?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
series of natural numbers
anonymous
  • anonymous
But, I no get (k+1) part
amistre64
  • amistre64
proving that if its true for one step; its true for every step

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
for me you have to identify whta is the successor of 1, and it is 0, so 1 is the successor of k
anonymous
  • anonymous
oops sorry
anonymous
  • anonymous
So, if n=1 is true, then (k+1) should be true?
anonymous
  • anonymous
No.
amistre64
  • amistre64
you havent really asked that detailed of a question; youre keeping secrets
anonymous
  • anonymous
The series of natural numbers, can all be defined if we know what we mean by the three terms "0," "number", and "successor." But we may go a step farther: we can define all the natural numbers if we know what we mean by "0" and "successor." It will help us to understand the difference between finite and infinite to see how this can be done, and why the method by which it is done cannot be extended beyond the finite. We will not yet consider how "0" and "successor" are to be defined: we will for the moment assume that we know what these terms mean, and show how thence all other natural numbers can be obtained.
watchmath
  • watchmath
Have you seen a domino effect? that's how you should think about induction.
anonymous
  • anonymous
Oops, didn't know you needed example. I sorry :) I give you example :) One moment, please
anonymous
  • anonymous
1 + 2 + 3 + . . . + n = ┬Żn(n + 1)
anonymous
  • anonymous
The logic is: It's true for n= (for example) 1 AND you can prove truth for n=k implies truth for n=k+1) THEN It's true for n = 1, 2, 3.....
amistre64
  • amistre64
n(n+1) ------ ah yes 2
amistre64
  • amistre64
gausses fame..
anonymous
  • anonymous
[Oh fun fact that isn't why Gauss is famous]
watchmath
  • watchmath
Translating INewton logic into domino logic: How to make all the domino fall. 1) Make sure the 1st domino fall. 2) Make sure that whenever the kth domino fall, the (k+1)th domino fall as well. If you can ensure that then all dominos will fall :).
amistre64
  • amistre64
n=2; 1+2 = 3 ; 2(2+1)/2 = 3
anonymous
  • anonymous
............ THAT GREAT IDEA!!!!! :DDDDD
amistre64
  • amistre64
its why I know gauss tho lol
amistre64
  • amistre64
n = 3; 1+2+3 = 6 ; 3(3+1)/2 = 12/2 = 6
anonymous
  • anonymous
Gauss Fact #1: Erdos believed God had a book of all perfect mathematical proofs. God believes Gauss has such a book.
anonymous
  • anonymous
Gauss field equations
anonymous
  • anonymous
Gauss Fact #2: Gauss checked the infinity of primes by counting them, starting from the last. Gauss Fact #3: Gauss considers infinity as the first non-trivial case in a proof by induction.
anonymous
  • anonymous
\[ \text{Assume } \sum^k_{r=1}r = \frac{k(k+1)}{2}\] \[ \text{Assume } \sum^{k+1}_{r=1}r = \sum^k_{r=1}r + (k+1) = \frac{k(k+1)}{2} + (k+1) = \frac{k(k+1)+2(k+1)}{2} \] \[=\frac{(k+1)[(k+1)+1]}{2} \] By mathematical induction blah...
watchmath
  • watchmath
I think the second word of "assume" shouldn't be there.
anonymous
  • anonymous
It shouldn't, lazy copy and past, ugh.... sorry.
anonymous
  • anonymous
paste*. I should have used \[\implies \] to start that line.

Looking for something else?

Not the answer you are looking for? Search for more explanations.